LaTeX to CAS translator
This mockup demonstrates the concept of TeX to Computer Algebra System (CAS) conversion.
The demo-application converts LaTeX functions which directly translate to CAS counterparts.
Functions without explicit CAS support are available for translation via a DRMF package (under development).
The following LaTeX input ...
{\displaystyle Q_n(x) = \begin{cases} \frac{1}{2} \log \frac{1+x}{1-x} & n = 0 \\ P_1(x) Q_0(x) - 1 & n = 1 \\ \frac{2n-1}{n} x Q_{n-1}(x) - \frac{n-1}{n} Q_{n-2}(x) & n \geq 2 \,. \end{cases} }
... is translated to the CAS output ...
Semantic latex: \assLegendreQ{n}@{x} = \begin{cases}\frac{1}{2} \log \frac{1+x}{1-x} & n = 0 \LegendrepolyP{1}@{x} \assLegendreQ{0}@{x} - 1 n = 1 \frac{2n-1}{n} x \assLegendreQ{n-1}@{x} - \frac{n-1}{n} \assLegendreQ{n-2}@{x} n \geq 2 .\end{cases}
Confidence: 0.63080360740902
Mathematica
Translation: LegendreQ[n, 0, 3, x] ==
Information
Free variables
- n
- x
Symbol info
- Legendre function of second kind; Example: \assLegendreQ{\nu}@{z}
Will be translated to: LegendreQ[$0, 0, 3, $1] Branch Cuts: (-\infty, 1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/14.2#i Mathematica: https://reference.wolfram.com/language/ref/LegendreQ.html
Tests
Symbolic
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \assLegendreQ [\assLegendreQ]
Tests
Symbolic
Numeric
Maple
Translation: LegendreQ(n, x) =
Information
Free variables
- n
- x
Symbol info
- Legendre function of second kind; Example: \assLegendreQ{\nu}@{z}
Will be translated to: LegendreQ($0, $1) Branch Cuts: (-\infty, 1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/14.2#i Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=LegendreQ
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Complete translation information:
{
"id" : "FORMULA_4ad16ba52f07a0747cc1caf916ae6d51",
"formula" : "Q_n(x)\n=\n\\begin{cases}\n \\frac{1}{2} \\log \\frac{1+x}{1-x}\n & n = 0\n \\\\\n P_1(x) Q_0(x) - 1\n & n = 1\n \\\\\n \\frac{2n-1}{n} x Q_{n-1}(x) - \\frac{n-1}{n} Q_{n-2}(x)\n & n \\geq 2 .\n\\end{cases}",
"semanticFormula" : "\\assLegendreQ{n}@{x} = \\begin{cases}\\frac{1}{2} \\log \\frac{1+x}{1-x}\n & n = 0 \\LegendrepolyP{1}@{x} \\assLegendreQ{0}@{x} - 1 n = 1 \\frac{2n-1}{n} x \\assLegendreQ{n-1}@{x} - \\frac{n-1}{n} \\assLegendreQ{n-2}@{x} n \\geq 2 .\\end{cases}",
"confidence" : 0.6308036074090242,
"translations" : {
"Mathematica" : {
"translation" : "LegendreQ[n, 0, 3, x] == ",
"translationInformation" : {
"freeVariables" : [ "n", "x" ],
"tokenTranslations" : {
"\\assLegendreQ" : "Legendre function of second kind; Example: \\assLegendreQ{\\nu}@{z}\nWill be translated to: LegendreQ[$0, 0, 3, $1]\nBranch Cuts: (-\\infty, 1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/14.2#i\nMathematica: https://reference.wolfram.com/language/ref/LegendreQ.html"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
},
"SymPy" : {
"translation" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\assLegendreQ [\\assLegendreQ]"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
},
"Maple" : {
"translation" : "LegendreQ(n, x) = ",
"translationInformation" : {
"freeVariables" : [ "n", "x" ],
"tokenTranslations" : {
"\\assLegendreQ" : "Legendre function of second kind; Example: \\assLegendreQ{\\nu}@{z}\nWill be translated to: LegendreQ($0, $1)\nBranch Cuts: (-\\infty, 1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/14.2#i\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=LegendreQ"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
}
},
"positions" : [ ],
"includes" : [ "Q_n(x)=\\begin{cases} \\frac{1}{2} \\log \\frac{1+x}{1-x} & n = 0 \\\\ P_1(x) Q_0(x) - 1 & n = 1 \\\\ \\frac{2n-1}{n} x Q_{n-1}(x) - \\frac{n-1}{n} Q_{n-2}(x) & n \\geq 2 \\,.\\end{cases}", "P_{n}", "Q", "P_s", "P", "Q_{n}", "-1" ],
"isPartOf" : [ "Q_n(x)=\\begin{cases} \\frac{1}{2} \\log \\frac{1+x}{1-x} & n = 0 \\\\ P_1(x) Q_0(x) - 1 & n = 1 \\\\ \\frac{2n-1}{n} x Q_{n-1}(x) - \\frac{n-1}{n} Q_{n-2}(x) & n \\geq 2 \\,.\\end{cases}" ],
"definiens" : [ ]
}